But in this hypothetical scenario they're not donating to a political campaign, they're buying advertising space directly from a private organization.

I suppose you could argue that ads which advocate for a political candidate could count as a "thing of value" for that candidate, but even in that case, there _is_ no foreign national to punish here; the entity that funded the effort is a foreign government, not an individual person.

One doesn't have to donate to a political campaign to contribute a "thing of value" to a campaign, that argument is elaborated on in the link I shared. The law does not define thing of value to be a donation or monetary contribution to a campaign, but something much broader, see 52 U.S.C. § 30121.

Likewise, foreign national is a legal term that includes foreign principals, which includes governments, see 22 U.S.C. § 611.